I A spaceship traveling close to the speed of light sending some data...

Staff: Mentor

If the spaceship were approaching Earth the data would arrive faster then once per second due to the decreasing distance the signal has to travel.

This is the Doppler effect, not time dilation. They are related but not the same. Time dilation is what you get when you take this direct observation and correct for the travel time of the light signals in order to calculate the rate at which they were emitted by the source. That rate will still be slower for an approaching source; the "slower" is time dilation.

An article celebrating the centennial of SR in a 2005 issue of “Discover” Magazine cited an example of time dilation using a moving railroad car and a flashlight. In the example, the conductor flashed a beam of light from the rear of the moving car toward the front. As the beam traveled forward with respect to the train’s direction, the front of the car receded from the oncoming light. Therefore, from the point of view of a trackside observer, the light took longer to traverse the moving car than it would have had the train been standing still on the tracks. Considering the time it took the light to make the journey as one unit of time on the train, the trackside observer would interpret the train’s “clock” as running “too slow”.

But again, this example was carefully chosen to illustrate the desired point. Had the conductor flashed the light backward with respect to the train’s motion, the forward-moving rear of the car would have intercepted the oncoming light sooner than it would have were the train motionless on the tracks. In this case, the trackside observer would see the light taking a shorter time for the experiment, and would interpret the train’s “clock” as running “too fast”

An article celebrating the centennial of SR in a 2005 issue of “Discover” Magazine cited an example of time dilation using a moving railroad car and a flashlight. In the example, the conductor flashed a beam of light from the rear of the moving car toward the front. As the beam traveled forward with respect to the train’s direction, the front of the car receded from the oncoming light. Therefore, from the point of view of a trackside observer, the light took longer to traverse the moving car than it would have had the train been standing still on the tracks. Considering the time it took the light to make the journey as one unit of time on the train, the trackside observer would interpret the train’s “clock” as running “too slow”.

But again, this example was carefully chosen to illustrate the desired point. Had the conductor flashed the light backward with respect to the train’s motion, the forward-moving rear of the car would have intercepted the oncoming light sooner than it would have were the train motionless on the tracks. In this case, the trackside observer would see the light taking a shorter time for the experiment, and would interpret the train’s “clock” as running “too fast”

Yes, but Discover magazine is hardly a reliable source for these matters. You won't find this sort of error in any serious text book.

Had the conductor flashed the light backward with respect to the train’s motion, the forward-moving rear of the car would have intercepted the oncoming light sooner than it would have were the train motionless on the tracks.

In this case, the trackside observer would see the light taking a shorter time for the experiment, and would interpret the train’s “clock” as running “too fast”

No, he would interpret it as relativity of simultaneity: light beams which would reach the ends of a motionless train simultaneously--or, equivalently, would reach the points on the track which would mark the ends of a motionless train simultaneously--do not reach the ends of a moving train simultaneously.

So a proper criticism of the argument, at least as you are presenting it here, is that the experiment is not about time dilation at all; it's about relativity of simultaneity. Neither the "forward" nor the "reverse" aspects of the scenario have anything to do with time dilation. To demonstrate time dilation, you would need a light pulse that goes out and comes back, as in a light clock, or some equivalent way of comparing clock rates.

To know whether the actual article is in fact making this mistake, I would have to see the article itself. It's quite possible that it is, since Discover magazine is not exactly a gold-plated source for relativity physics; but it's also possible that you are misinterpreting the argument given in the actual article.

Yes, but Discover magazine is hardly a reliable source for these matters. You won't find this sort of error in any serious text book.

How about "The Universe and Dr. Einstein" by Lincoln Barnett with a forward by Dr. Einstein himself? Serious enough for you? In Chapter 6, using the train-and-lightening thought experiment, he claims that the observer riding at the midpoint of the train will see the forward strike before seeing the rear strike. Not so. Since the train is an inertial reference frame it can be considered "at rest" while the countryside rushes past. SR says that the measured speed of light is the same for all observers. This includes the observer on the train. It is the trackside observer who sees the front strike reaching the train observer first, not the train observer himself.

This isn't the example of the error I originally posed, but it is another false conclusion from a "serious" source.

How about "The Universe and Dr. Einstein" by Lincoln Barnett with a forward by Dr. Einstein himself? Serious enough for you? In Chapter 6, using the train-and-lightening thought experiment, he claims that the observer riding at the midpoint of the train will see the forward strike before seeing the rear strike. Not so. Since the train is an inertial reference frame it can be considered "at rest" while the countryside rushes past. SR says that the measured speed of light is the same for all observers. This includes the observer on the train. It is the trackside observer who sees the front strike reaching the train observer first, not the train observer himself.

This isn't the example of the error I originally posed, but it is another false conclusion from a "serious" source.

No it isn't. It is you who are misinterpreting things. You need to be careful about specifying in what frame the lightning strikes are simultaneous. You cannot just say "simultaneous" without any qualifier that tells you what frame they are simultaneous in. If they are simultaneous in the ground's rest frame, the observer on the train will see the front strike first. This must be true in all reference frames and since the speed of light is the same in all directions, the strikes must therefore occur at different times in the train's rest frame.

If the strikes are simultaneous in the train's rest frame, then the ground observer will see the back strike first.

It is the trackside observer who sees the front strike reaching the train observer first, not the train observer himself.

The sequence with which an observer sees (with his eyes) a set of flashes is an invariant physical fact. All observers agree on it. If two strikes are simultaneous in the trackside observer's frame then it will be a physical fact of the matter that the midpoint observer on the train will see the front flash first.

The two observers can and do account for that fact in different ways. The train observer will say that it is because the flashes were not simultaneous. The trackside observer will say that it is because the train observer moved toward one flash and away from the other.

This isn't the example of the error I originally posed, but it is another false conclusion from a "serious" source.

But you've yet to establish your first claim that there was a false conclusion from a serious source.

It could very well be that the the writer of the Discover article made an error in his explanation of time dilation, as you originally claimed. But we don't know.

In your second claim about the relativity of simultaneity it is you who has made the error. It's possible for those two events be simultaneous in either frame, but not both. Because the two frames are equivalent.

No it isn't. It is you who are misinterpreting things. You need to be careful about specifying in what frame the lightning strikes are simultaneous. You cannot just say "simultaneous" without any qualifier that tells you what frame they are simultaneous in. If they are simultaneous in the ground's rest frame, the observer on the train will see the front strike first. This must be true in all reference frames and since the speed of light is the same in all directions, the strikes must therefore occur at different times in the train's rest frame.

If the strikes are simultaneous in the train's rest frame, then the ground observer will see the back strike first.

This is my last response. Obviously, you are simply bent on being argumentative. If you read my description you will see than I never used the term "simultaneous'. I made quite clear the difference between what the train observer sees and what the trackside observer thinks the train observer sees. In fact, if you read the book you will see that the author made exactly the same mistake you falsely accuse me of making. "A thunderstorm breaks, and two bolts of lightening strike the track simultaneously at different points."

That's all I have to say. I think you just want to argue. I don't. Adios.

This is my last response. Obviously, you are simply bent on being argumentative. If you read my description you will see than I never used the term "simultaneous'. I made quite clear the difference between what the train observer sees and what the trackside observer thinks the train observer sees. In fact, if you read the book you will see that the author made exactly the same mistake you falsely accuse me of making. "A thunderstorm breaks, and two bolts of lightening strike the track simultaneously at different points."

That's all I have to say. I think you just want to argue. I don't. Adios.

I am sorry you feel this way. But consider that essentially everyone in this thread knows relativity much better than you do. From the perspective of those who actually know the subject, it is you who are being argumentative and hell-bent on not accepting conclusions that have been scrutinised by 100 years worth of physicists and that agree very well with experiments.

In fact, if you read the book you will see that the author made exactly the same mistake you falsely accuse me of making. "A thunderstorm breaks, and two bolts of lightening strike the track simultaneously at different points."

In popular literature, such assumptions will often be implicit. Since it is saying "strike the track simultaneously", the natural assumption would be to assume that this refers to the track's rest frame. You are making exactly the error of assuming that simultaneous in one frame means simultaneous in all frames. In fact, this is exactly what this thought experiment shows: Assuming that the light speed is the same in all directions in all inertial frames, the events cannot be simultaneous in the train's frame if they are simultaneous in the track's frame. This thought experiment by itself is not showing time dilation, it is showing relativity of simultaneity (although it is necessary to understand relative simultaneity if you want to understand why time dilation is symmetric).

Staff: Mentor

Since the train is an inertial reference frame it can be considered "at rest" while the countryside rushes past.

Yes, but in this frame the light rays are emitted at different times, which is why they are received at different times by the observer at the center of the train. Same speed, same distance, different emission times = different reception times.

Hmm; have you ever wondered why these age-old thought experiments, the light from two 'simultaneous' lightning strikes or alternatively light from a single source in the middle of the train, continue to cause so much discussion and dissension?

The basic premise is the simple one set out by Einstein in Chapter IX The Relativity of Simultaneity; observers at rest upon the embankment will observe the lights meeting at midpoint M proving that events A & B were simultaneous in their frame of reference. Observers at M' on the train '(considered with reference to the railway embankment)' are moving away from point M and therefore will not measure simultaneity.

All very simple and straightforward. So how do all the difficult questions arise?

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Is there not something fundamental that is being overlooked here? - The change in perspective that Einstein introduced with his theories.
A fundamental change introduced with the theory of relativity was from the Objective 'God-like' view of what was being measured to the Subjective view of specific observers. Not surprisingly different observers make different measurements. Science suddenly changed from observing a single overall view to taking multiple different perspectives of different observers while still trying to present a single reality.

Nothing is fixed anymore it all depends on the relative movement of the observer and the observed.

So perhaps it would be better to examine what happens objectively and then calculate how this would be seen subjectively from different frames of reference.

Objectively: Light from two events A, B meet at event M. AM = BM so the light has travelled equal times at c from each source; therefore events A and B are simultaneous from an objective point of view. What do I mean by that? Well, they are simultaneous measured using the rods and clocks of the resting frame; i.e. measured by any observer at rest relative to events A, B and M.

But, subjectively, every observer is at rest relative to Spacetime - as mapped by their frame of reference in which they are by default at the origin or null point.
So for any observer present at M when events A and B occur will remain at M at the origin or null point of their frame of reference.

Taking any particular view such as the embankment and giving that the status of being the only truth is making it the privileged view. Einstein avoided that when he added

Objectively: Light from two events A, B meet at event M. AM = BM so the light has travelled equal times at c from each source; therefore events A and B are simultaneous from an objective point of view. What do I mean by that? Well, they are simultaneous measured using the rods and clocks of the resting frame; i.e. measured by any observer at rest relative to events A, B and M.

Observers at rest on board the train can make the same claim. They can use rods and clocks of their resting frame to show that any observer at rest relative to events A, B, and M will see them as not being simultaneous. All you need to do is have the lightning strikes leave burn marks on both the train and the embankement. Likewise you can have an explosion occur at M that leaves the same type of burn marks.

Hmm; have you ever wondered why these age-old thought experiments, the light from two 'simultaneous' lightning strikes or alternatively light from a single source in the middle of the train, continue to cause so much discussion and dissension?

Lots of research has been done in an attempt to understand and improve student understanding of this and many other topics. But wondering why most people find it difficult to understand many of the topics of physics doesn't change the fact that they do.

Relativity of simultaneity is not demonstrated experimentally by this thought experiment. It is demonstrated every minute of every day at hundreds of places across the globe by scientists, engineers, and technicians who deal with precision timing, fast-moving particles, or both. It is not the human intellect that demonstrates the validity of this or any other physics concept, rather it is Nature's behavior.

This is correct; in fact it is the key objective fact about the entire scenario. And furthermore, this objective fact does pick out one particular inertial frame among all the possible ones. But you are not correctly describing how that frame is picked out, or what the implications are.

Having a frame in which you are at rest does not make you "at rest relative to spacetime"; the latter concept doesn't even make sense.

Apologies for the use of hyperbole; for of course events are points fixed in space and time; but what do we mean by 'at rest'?
Surely that can only be relative to a frame of reference - for when we refer to a point or body, or any Minkowski 'substantial point' it is has to be located within a frame of reference.
Any Frame of Reference gives a fixed map relative to the event at its origin, or null point; a map in which everything in Spacetime is moving relative to that frame of reference.
It is a somewhat tautological concept but every observer must be at rest relative to their frame of reference.

Observers at rest on board the train can make the same claim. They can use rods and clocks of their resting frame to show that any observer at rest relative to events A, B, and M will see them as not being simultaneous.

Exactly! For then it is an observer from another frame for whom the train is moving. But the observer on the train, in his frame of reference is at rest and for him A, B and M' will be fixed points and AM' = M'B. For the train observer it is M and the embankment that is moving away.

The train observer will measure simultaneity but for them it is the embankment observer who is moving away and therefore won't.

Apologies for the use of hyperbole; for of course events are points fixed in space and time; but what do we mean by 'at rest'?
Surely that can only be relative to a frame of reference - for when we refer to a point or body, or any Minkowski 'substantial point' it is has to be located within a frame of reference.
Any Frame of Reference gives a fixed map relative to the event at its origin, or null point; a map in which everything in Spacetime is moving relative to that frame of reference.
It is a somewhat tautological concept but every observer must be at rest relative to their frame of reference.

You are missing the entire point. Events are single points in space-time and cannot be assigned a state of motion. In order to assign a state of motion, you need to consider the world line of an observer, which is an extended one-dimensional curve in space-time.

In order to assign a state of motion, you need to consider the world line of an observer, which is an extended one-dimensional curve in space-time.

Maybe we can arrange these notions this way. I think that to be “at rest” means to introduce your own rest frame with Einstein synchronized clocks, as we do in Special Relativity. An observer cannot detect his absolute motion, but can subjectively assign himself this state. What actions he has to take, if he assigns himself state of motion? What his actions should be different from those, when observer assigns himself state of rest?

1) He shouldn’t introduce his own reference frame with synchronized clocks, but has to use other guy’s one. For example, there is a reference frame K with Einstein – synchronized clocks A and B. In this reference frame moves clock C. Observer "in motion" possesses clock C and compares readings of this clock with clock A first and clock B then (successively).

2) If an observer ascribes himself state of rest, he introduces his own reference frame and adds another clock D into another spatial position. He synchronizes clocks C and D by Einstein. Clock A (and then clock B) now moves in his reference frame. Then he compares readings of clock A with clock C first and clock B then. Obviously, clock A dilates. So, if we describe motion and use just one reference frame, we need 3 (three) clocks. If there are two reference frames and each is "at rest", we need 4 (four) clocks.

3) Let’s observer ascribes himself state of rest. Then another observer or observable object (source of light, for example) moves at parallel line to axis X in observer’s frame. In this case the observer, who assigns himself state of rest has to accept beams of light that were released, when this observer and source WERE at points of closest approach. If he has a telescope, he keeps his telescope along Y axis straight up.

4) If observer ascribes himself state of motion in other guy’s reference frame, he accepts beams of light, when he and observable object ARE at the points of closest approach. In this case he keeps his telescope at oblique angle to direction of his motion “into front”. The source appears to be in the front of him, though actually is straight “under” him at points of closest approach. He thinks that he keeps his telescope at oblique angle in order to take into account aberration of light, as astronomers do observing distant stars.

It should be noted, that if two observes move relatively to each other, they cannot ascribe themselves equal states simultaneously. Of one assigns himself state of rest, another has to assign himself state of motion. For example, if one observer releases beam of light straight up along y axis, another one, who moves in his frame, has to tilt his telescope at oblique angle to direction of his motion “into front”. They can calculate these angles using aberration of light formula.

You are missing the entire point. Events are single points in space-time and cannot be assigned a state of motion. In order to assign a state of motion, you need to consider the world line of an observer, which is an extended one-dimensional curve in space-time.

I'm sorry I don't understand what you mean here. '... In order to assign a state of motion ...' - in order to assign a state of motion to what? An Event? But as you have just stated viz. ' Events are single points in space-time and cannot be assigned a state of motion. ' ...???